Recently, [1]} also study a variant of the problem GD-FixedPoint. The focus of their paper is on \(1/(n)\)  or even constant approximation, whereas we seek exponentially precise approximation. Note that for GD-FixedPoint, it is easy to compute a \(1/(n)\) -approximate fixed point in polynomial time because the potential is bounded. In contrast, for the gradient descent-ascent dynamics (GDA-FixedPoint) the potential may increase and decrease alternatingly, which makes the problem much harder for approximation.
Indeed, for an even harder variant of approximate GDA-FixedPoint where the domain is not a cartesian product, [1]} prove that the problem is -complete. (Approximate GDA-FixedPoint over e.g. the hypercube remains an exciting open problem.)
